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Draw the perpendicular bisectors of any two sides which are not directly opposite one another. These will meet at the centre of the circle.


If it has an even number of vertices, simply join two pair of opposite vertices. They will intersect at the centre of the circle.

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Q: If given any regular polygon how can you find the center of the circle that circumscribes the polygon?
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The figure is a regular 12-sided polygonthe diameter of the circle that circumscribes it is 16cmfind the radius of the polygon?

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Circumcenter - the center of the circle that circumscribes the triangle, ie. goes through all its vertices.


How is an apothem different from a radius?

An apothem is a line drawn perpendicular to a side of a regular polygon from the center of the polygon. A polygon is not a circle so it cannot have a radius. The radius of a circle is drawn from the center to any point in the circumference of the circle. You can draw a circle which encloses the regular polygon touching all vertices. The polygon is said to be inscribed in the circle. The apothem will be less than the radius because the radius is not perpendicular to any side, it can be drawn to a vertex but the apothem is perpendicular to a side, so it is shorter. Ex: draw a square with a circle which inscribes it. You can see that the apothem will be less than the radius.


How do you find out if the polygon of a circle is regular or not?

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Is a semi circle a regular polygon?

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